Find acceleration from two distances and times - SUVAT

How could you find acceleration from two distances and two times, i.e the question is: The distance OA is 64m and OB is 250m. The car passes point O at 0 seconds, A at 2 seconds and B at 5 seconds. Acceleration is constant. The car however does not have 0 velocity (U) at O because 'the car is emerging from a bend before it reaches O which is a straight piece of road'. How would you solve this to find acceleration and then the speed of the car at B. It is straight road. Thank you!

How could you find acceleration from two distances and two times, i.e the question is: The distance OA is 64m and OB is 250m. The car passes point O at 0 seconds, A at 2 seconds and B at 5 seconds. Acceleration is constant. The car however does not have 0 velocity (U) at O because 'the car is emerging from a bend before it reaches O which is a straight piece of road'. How would you solve this to find acceleration and then the speed of the car at B. It is straight road. Thank you!

It is useful to split this into two different scenario's: motion for OA and motion for AB.

OA:

$s=64$

$u=u$

$v=u+at$

$a=a$

$t=2$

AB:

$S=250-64=186$

$U=u+at$

$V=U+AT$

$A=a$

$T=3$

Can you see where to go from there?

It is useful to split this into two different scenario's: motion for OA and motion for AB.

OA:

$s=64$

$u=u$

$v=u+at$

$a=a$

$t=2$

AB:

$S=250-64=186$

$U=u+at$

$V=U+AT$

$A=a$

$T=3$

Can you see where to go from there?

I completely understand what you've written but I'm not sure how to go from there as we do not know u???

I completely understand what you've written but I'm not sure how to go from there as we do not know u???

Sorry I am confused, can we only find an average speed for u, as the car is accelerating??

You can use $s=\frac{1}{2}(u+v)t$ and use substitutions for the final speed in terms of initial speed and acceleration.

For OA:

$64=\frac{1}{2}(u+v)(2)=u+(u+at)=2u+2a$

For AB:

$186=\frac{1}{2}(U+V)(3)=\frac{3}{2}[(u+2a)+(u+2a+3a)]$

Tidy it up and you have two simultaneous equations in u and a to solve.

This is overcomplicating things.

$64=2u+2a$

This can come straight from $s=ut+\frac{1}{2}at^2$ instead of using two SUVAT equations.

And the second equation is simple if you consider OB instead of AB.

Meh, I wouldn't say using substitutions is very over complicating things, but okay, up to him what he wants to do as long as he understands the method he uses and does it correctly.

In this case I don't agree. Mechanics students should be encouraged to look for the simplest method to minimise errors.

Most M1 students who try your method would end up in a mess. And there's definitely no need to use two SUVAT equations.